动量二次循环系统的积分

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Regular and Chaotic Dynamics Pub Date : 2021-12-06 DOI:10.1134/S1560354721060046

Valery V. Kozlov

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引用次数: 2

摘要

本文讨论了当外力为非势时，二次速度(动量)循环系统守恒定律(第一积分)存在的条件问题。在一定条件下，将运动方程简化为具有辛结构的哈密顿形式，用二次积分代替哈密顿形式。在某些情况下，方程被简化为共形哈密顿形式而不是哈密顿形式。二次积分的存在及其性质使我们可以得出循环系统平衡位置稳定性的结论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Integrals of Circulatory Systems Which are Quadratic in Momenta

This paper addresses the problem of conditions for the existence of conservation laws (first integrals) of circulatory systems which are quadratic in velocities (momenta), when the external forces are nonpotential. Under some conditions the equations of motion are reduced to Hamiltonian form with some symplectic structure and the role of the Hamiltonian is played by a quadratic integral. In some cases the equations are reduced to a conformally Hamiltonian rather than Hamiltonian form. The existence of a quadratic integral and its properties allow conclusions to be drawn on the stability of equilibrium positions of circulatory systems.

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.